I would talk to you're sister. Ask her why she is doing that. You can go to Radio Shack and get a really cheap voice recorder and record her. explain that what she has said was a lie. And when she confesses to you. Make sure she is alone when you ask her so that she will feel comfortable to give you a hard time. Then you will have the proof that she is dishonest. Then get the parents involved and explain that what you have been saying is the truth and you would not believe me so I had to prove my side of what has been really been going on. and say I know this is not fair to her when I recorded her but that this was the only way you you to listen to me. And she has some serious issues about lying. If she is lying about you what else is she covering up.
Well I'm glad someone's having the same problem i was getting into **** all the time my little sister would do something till I caught the little devil with my camera stealing $10 from my mom and it was the best day of my life when I showed her